I thought this article was an interesting insight into the thought process of those who disregard the relevance of neuroscience for understanding the mind. The terminology Lehrer uses gives him away:
Even our sense of consciousness is explained away with references to some obscure property of the frontal cortex.
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[According to reductionism]The mind, in other words, is just a particular trick of matter, reducible to the callous laws of physics.
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You are simply an elaborate cognitive illusion, an “epiphenomenon” of the cortex. Our mystery is denied.
All of these quotes highlight a curiosity in Lehrer’s phrasing. Does he really think that if neuroscience succeeds in explaining cognitive phenomena in mechanistic terms, the mind will be “explained away”? Was heat “explained away” when we reduced it to the movement of molecules? Were the properties of water “explained away” when we reduced it to H2O? On the contrary, the phenomena of both are still with us and it is ridiculous to assume that if neuroscience is successful it will reduce the mind to “just a trick”. On the contrary, the mind will be seen as a complicated set of cognitive phenomena not just “reducible to” but explained by mechanisms in the brain/body system.
So, the question isn’t as Lehrer says whether or not neuroscience can move “beyond reductionism”, but rather, what can be successfully explained in mechanistic terms and what can’t? It is clear that there is useful phenomenological data to be had at the higher levels of abstractions that characterize our thoughts about the mind, but it should be said again that these abstractions aren’t “just” tricks, but rather, complicated phenomena in their own right that need explaining. Whether or not that explanation will be in the terms of neuroscience or at the higher level of cognitive psychology has yet to be determined, but it seems clear that the empirical method itself will give us a clearer picture of the mind.
This brings me to my last point, and that is whether or not neuroscience is capable, in principle, of explaining all cognitive phenomena. For me, the answer is a resolute yes, but I want to emphasize the term “in principle”, because explaining all cognitive phenomena at the molecular level may be pragmatically out of reach. We should be grateful that evolution has given us a language capable of discussing cognitive phenomena at a higher abstraction than that of science, but we should also learn to accept the fact that ultimately everything in the universe, including the mind, can be “reduced” to the physical motions of matter. It might seem like I am making a category mistake, but it seems intuitively plausible to me. I am not saying that all cognitive phenomena will be reduced to the physical level, but I think in principle, it can be. But I don’t think that is a very interesting idea. What is more interesting to me is the question of what will be explained in mechanistic terms and what won’t, and that is a pragmatic question of science that we will be continuously working on for what seems like an indefinite period of time.
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Minds and Brains 
Good critique. Plus, his analysis of the ‘antireductionistic’ blue brain project is reductionism writ large: try to understand large-scale cortical dynamics by modelling each individual cell in great detail!
Yeah, that was the part that confused me the most. He has an article in the latest SEED magazine about the Blue Brain Project and he echoes similar rhetoric, although not to the extent that he does in this article. It is an interesting read nevertheless. Something I didn’t know was that the researchers are going to try and embody the simulation in a robotic rat. I think this will be the ultimate benchmark for the project. Hopefully this happens sooner rather than later.